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 Algebra i Analiz: Year: Volume: Issue: Page: Find

 Algebra i Analiz, 2014, Volume 26, Issue 5, Pages 64–87 (Mi aa1397)

Research Papers

Realization and characterization of modulus of smoothness in weighted Lebesgue spaces

R. Akgünab

a Centre de Recerca Matemàtica (CRM), Campus de Bellaterra, Edifici C, 08193, Bellaterra, Barcelona, Spain
b Balikesir University, Faculty of Arts and Sciences, Department of Mathematics, ÇağIş Yerleşkesi, 10145, Balikesir, Türkiye

Abstract: A characterization is obtained for the modulus of smoothness of fractional order in the Lebesgue spaces $L_\omega^p$, $1<p<\infty$, with weights $\omega$ satisfying the Muckenhoupt $A_p$ condition. Also, a realization result and the equivalence between the modulus of smoothness and the Peetre $K$-functional are proved in $L_\omega^p$ for $1<p<\infty$ and $\omega\in A_p$.

Keywords: fractional modulus of smoothness, realization, muckenhoupt weight, characterization, $K$-functional.

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English version:
St. Petersburg Mathematical Journal, 2015, 26:5, 741–756

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Citation: R. Akgün, “Realization and characterization of modulus of smoothness in weighted Lebesgue spaces”, Algebra i Analiz, 26:5 (2014), 64–87; St. Petersburg Math. J., 26:5 (2015), 741–756

Citation in format AMSBIB
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\paper Realization and characterization of modulus of smoothness in weighted Lebesgue spaces
\jour Algebra i Analiz
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\vol 26
\issue 5
\pages 64--87
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\jour St. Petersburg Math. J.
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\issue 5
\pages 741--756
\crossref{https://doi.org/10.1090/spmj/1356}
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• http://mi.mathnet.ru/eng/aa/v26/i5/p64

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. R. Akgun ., “Mixed modulus of continuity in the Lebesgue spaces with Muckenhoupt weights and their properties”, Turk. J. Math., 40:6 (2016), 1169–1192
2. Yu. Kolomoitsev, “On moduli of smoothness and averaged differences of fractional order”, Fract. Calc. Appl. Anal., 20:4 (2017), 988–1009
3. R. Akgun, “Gadjieva's conjecture, $K$ -functionals, and some applications in weighted Lebesgue spaces”, Turk. J. Math., 42:3 (2018), 1484–1503
4. Akgun R., “Mixed Modulus of Smoothness With Muckenhoupt Weights and Approximation By Angle”, Complex Var. Elliptic Equ., 64:2 (2019), 330–351
5. Jafarov S.Z., “Derivatives of Trigonometric Polynomials and Converse Theorem of the Constructive Theory of Functions in Morrey Spaces”, Proc. Inst. Math. Mech., 45:1 (2019), 137–145
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